Piaget's Stage (Part 2)

Third Stage: Concrete Operations
In the concrete operational stage, which cover roughly the age from 7 to 11, the child becomes capable of various logical operations, but only with concrete things. An operation is a type of action-a manipulation of objects or their internal representations. It calls for transforming information so that it can be used more selectively. Operations make trial and error unnecessary because the child can think through the possibilities of certain actions and results of actions.
Operational thought replaces the impressionistic leaps from data to conclusions with a series of small scale, reversible steps, each of which can be judged as reasonable or unreasonable. if information is concrete, comparisons can be made accurately. Thus the child is not taken in by changed beaker shapes as liquid is poured back and forth. He can imagine operations and anticipate results. For example, until this stage is reached, the children can not tell you with any conviction what the other side of the moon is like. But in the stage of concrete operations he can, in his mind, manipulate the moon by turning it around and will tell you that it probably looks just like this side of the moon.
During this stage the child becomes able to handle classification systems like that shown in figure 3. This means that he becomes able to handle complex logical ideas such as:
  • composition, that is the idea that, whenever two elements of a system are combined (for example reciprocating-engine autos, A, and other autos, A'), we obtain other element of system (that is, autos, B). Or if we combine autos (B) and other means of transportation (B'), we obtain means of transportation (C).
  • associativity, the idea that the sum is independent of the order in which things are added. Thus in the example above, A + A' = B, and A' + A = B.
  • reversibility, the idea that not only can we add nonautos (B') with autos (B) to obtain means of transportation (C), but when we subtract nonautos from modes of transportation, we obtain autos.
Although the children can handle these classification, grouping and ordering problems, he is not fully aware of the principles involved. Nevertheless his thinking is at a very high level. He is not centered on some salient perceptual characteristics but can think through a number of problems independent of their perceptual dimensions. His limitation in this stage is the need for concrete representations to tie this thinking to. The seven-to-eleven-year old the child still has problems with highly abstract thought.

Figure 3
Classification Scheme showing kinds of operations that child can handle in the stage of concrete operations

Fourth Stage: Formal Operations

In the formal operational stage, which covers the ages from about 11 to 14, the student become capable of logical thinking with abstractions, that is, with the "possible" as well as the "here and now". Scientific thinking of hypothetico-deductive type is is now possible. He can draw conclusions, offer interpretations, and develop hypoteses. His thought has become flexible and powerful. He can:
  • work out all the logical possibilities, without needing to determine which ones actually occur in the real world. This capability refers not mere imagination, since younger children can engage in fanciful thinking, but to lawful and systematic exposition of logical alternatives. This means also that the student can
  • conduct a combinational analysis of possibilities. Thus, given two possible causes, C1 and C2, and a result, r, the student can formulate the possibilities that
    either C1 or C2 causes r,
    both C1 or C2 causes r,
    neither C1 or C2 causes r,
    C1 could cause r, but C2 could not,
    C2 could cause r, but C1 could not,
    C1 and C2 could cause r, but neither one alone could,
    C1 could cause r, but only if C2 is absent,
    and so on
  • do propositional thinking. Thus the adolescent can take propositions of the kind just stated about C1, C2, and r, and regard them as elements to be combined into new, higher order propositions, such as "either p1 or p2 can be true, but not both."
  • generalize from propositions based on one kind of content, say, clay or beads, to many other kinds of content, such as water, wood pieces, checkers, physical objects in general, all liquids, and all numerically denotable quantities.
The adolescent in possession of formal operational thought can organize information in markedly different ways than was possible when concrete operational thought was being used. For example, in one experiment of Inhelder and Piaget (1958), children were given four flasks that were perceptually similar, containing odorless, colorless liquid. The Flasks contained (1) diluted sulphuric acid, (2) water, (3) oxygenated water, and (4) thiosulfate. A bottle, with a dropper, containing potassium iodide is added and is called g. oxygenated water (3) oxidizes potassium iodide (g) in an acid medium (1). That is 1 + 3 + g wil l yielded a yellow color. The water (2) is neutral, so that color is not changed when it is added to a mixture. The thiosulfate (4) will bleach out the yellow mixture of 1 + 3 + g. In this situation the experimenter gives the subject two glasess. In one glass is the mixture 1 + 3. In other glass is 2. The subject is anaware of what combinations are in each of the glasses. While the subject watches, the experimenter puts several drops of g in each glass and notes the different ractions. The subject is asked to reproduce the same yellow effect using flasks 1, 2, 3, 4 and g in any way he wishes. Two records of two subjects in this experiment are given below. The first record (adapted from Inhelder & Piaget, 1958 p 111) is from a seven year old.
    Subject: (Tries 4 x g, then 2 x g, and then 3 x g). I think I did everything. I tried them all. Experimenter: What else could you have done? Subject: I don't know Experimenter: (Give the glasses to the subject again) Subject: (Repeats 1 x g, 2 x g, etc) Experimenter: You took each bottle separately. What else could you have done? Subject: Take two bottle at the same time. (Subject then tries 1 x 4 x g, then 2 x 3 x g, failing to cross over between the two sets of bottle: for example, 1 x 2, 1 x 3, 2 x 4, and 3 x 4, etc) Experimenter: (Suggests that subject add other bottles) Subject: (Puts 1 x g in the glass already containing 2 x 3, which results in the appearance of color) Experimenter: Try to make the color again Subject: Do I put in 2 or 3? (Subject tries with 2 x 4 x g, then adds 3, then tries it with 1 x 4 x 2 x g) I don't remember anymore.
The seven-year-old's behavior is not random. There are elements of systematic thought and organized planning activity that are considerably above the pre operational level of behavior. Still this seven-year-old's attempts are adequate. He could only deal with a few of the possible combination at once. Environmental support, such as the experimenter's hints and motivating statements, were needed to keep the subject searching for a solution. In contrast, we now present the record (adapted from Inhelder & Piaget, 1958, p. 117) of a fourteen-year-old facing the same problem, but being able to use formal operational thought.
    Subject: You have to try it with all the bottles. I'll begin with the one at the end. (Subject goes from 1 to 4 with g). It doesn't work anymore. Maybe I have to mix them. (Subject tries 1 x 2 x g, then 1 x 3 x g). it turn yellow. Experimenter: Are there other solutions? Subject: I'll try. (Subject tries all six combinations of flasks, taking two at a time). It doesn't work. It only works with 1 x 3 x g. Experimenter: Yes, and what about 2 and 4? Subject: 2 and 4 don't make any color together. They are negative. perhaps I could add 4 in 1 x 3 x g to see if it would cancel out the color. (The subject pours 4 into the yellow mixture). Liquid 4 cancel it all. I'll have to see if 2 has the same influence. (He pours 2 into mixture of 1 x 3 x g). No, it doesn't, so 2 and 4 are not alike because acts on 1 x 3 and 2 doesn't. Experimenter: What is there in 2 and 4? Subject: In 4 certainly water. No the opposite, in 2 certainly water since it didn't act on liquids. That makes things clearer. Experimenter: And if I were to tell you that 4 is water? Subject: If the liquid 4 is water, when you put it into 1 x 3 it wouldn't completely prevent the yellow from forming. It isn't water. It's something harmful.
The adolescent thought processes led him right at the start to cross all elements with all others. A method for determining causal relationship is used. His language is clearly hypothetico-deductive. He is thinking scientifically with "if ...then ... statement in mind. In Piaget theory, this kind of scientific thinking cannot be done by very young children. Only through experience and maturation does this kind of reasoning occur. This is important for teacher to know. The kind of adult logic that teachers possess may be unattainable by children before their adolescent years. Peel (1976) has evidence of continued change in the complexity of adolescent thinking through age 17, and there is little doubt that some kinds of cognitive functioning change even later than that. All this only means that we should be careful about the level of maturity we expect from our students in logic and scientific thinking.
The developmental process
How do the children behave so as to acquire these successive intellectual capabilities? In general, they engage in a process of seeking an equilibrium between what they presently perceive, know, and understand, on the one hand, and what they see in any new phenomenon, experience, or problem. If their present condition can handle the new situation, their equilibrium is undisturbed. If it cannot, then some intellectual is necessary to restore the equilibrium. That is, some adaptation by the organism to its environment must take place.
Adaptation takes two forms, which occur simultaneously: assimilation and accommodation. Assimilation is the process of changing what is perceived so that it fits present cognitive structures, while accommodation is the process of changing the cognitive structures so that they fit what is perceived.
Assimilation is comparable to the acts of chewing and digesting in order to transform food into something the body can use. Assimilation transforms new ideas into something that fits into one’s cognitive structure. Accommodation is comparable to the adjustments made by the body in eating and using food. Such as opening the mouth, contracting the muscles of the throat, esophagus, and stomach, and secreting the digestive juices. In the same way, an existing cognitive structure must be modified, extended, or refined in coming to grips with a new or anomalous idea.
Assimilation and accommodation may be hard to tell apart. They go on simultaneously and, in the processing of ideas, they are two sides of the same coin, the process of maintaining equilibrium between the person and his environment. When we interpret, construe, and structure, we are changing the nature of reality to make it fit into our own cognitive structure. This is assimilation. When we adjust our own ideas, as in calling up memory, a similarity, or analogy, in order to make sense of reality, we are accommodating.
The processes of assimilation and accommodation have somewhat lasting effects on the cognitive structures involved. As ways by which an organism adapts to its cognitive environment, they are comparable to the biological process of adaptation that affect the structure and functions of an organism’s body. So a child’s cognitive schema, that is, his cognitive organization and structure, gradually changes as a function of his experience. As children mature, they go through the four stage of cognitive development described above.

Educational Psychology. Gage, N.L & Berliner, David C.

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